Necessary existence criteria for mandatory representation designs MRD (4, k; ν)
✍ Scribed by Martin Grüttmüller; R. S. Rees
- Publisher
- John Wiley and Sons
- Year
- 2001
- Tongue
- English
- Weight
- 234 KB
- Volume
- 9
- Category
- Article
- ISSN
- 1063-8539
- DOI
- 10.1002/jcd.1014
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✦ Synopsis
Abstract
A mandatory representation design MRD (K; ν) is a pairwise balanced design on ν points with block sizes from the set K in which for each k ∈ K there is at least one block in the design of size k. A survey of known results on MRDs has been given in [J Comb Math Comb Comput, to appear] by Rees. MRDs with K = {3, k} have been extensively studied by Mendelsohn and Rees [J Comb Theory Ser A 49 ( 1988), 349–362], Rees [J Stat Plann Inference 86 (2000), 567–594], Rees and Grüttmüller [Congr Numerantium, 147 (2000), 41–51] and Grüttmüller [J Comb Des 8 (2000) 122–131; On the existence of pairwise balanced designs, Ph.D. Thesis, University of Rostock, 1999]. In this paper, we investigate necessary conditions for the existence of MRDs with K = {4, k}. © 2001 John Wiley & Sons, Inc. J Combin Designs 9: 309–333, 2001